In 1958, at the advanced age of 83, Jung published a book on UFOs. He told an interviewer that having studied them for "about 12 years ... I cannot even say whether they exist or not". He knew that even in addressing the topic he was risking, as he said, "his hard-won reputation for truthfulness, reliability and capacity for scientific judgement". But there was, he thought, at least one "remarkable fact" about UFOs worth the attention of someone of his profession: what were modern people in need of in their quest for extraterrestrial life? And yet when two close American friends went to Jung's home in Switzerland they were amazed to find the "sage of Zurich" telling them that flying saucers were "factual", and that he was not "in the least interested in psychological aspects ... or in factual information relating to the investigation of flying saucer reports". Jung was often, as he himself acknowledged, in at least two minds about things; and, as Deirdre Bair notes in her new and useful biography, he "never hesitated to explode in wrath when anyone crossed him". One of the things that seems to have made him most cross was the extent to which he was at war with himself. "Don't forget," he once said, in a memo rather more to himself than to anyone else, "I am definitely no philosopher, and my concepts are accordingly empirical and not speculative." It is an empirical fact that Jung, to his credit, was always more speculative than he wanted to be. Like everyone else, he hated being crossed because it exposed how at odds with himself he really was.

Science appealed to Jung because it seemed to offer some hope of a cure for the dividedness of his self; science kept alive the possibility that somewhere there was a consensus about what life was like, that somewhere and somehow there could be agreement about things. That nature, at least, could be an authority figure. Bair's story is a lengthy one, partly because Jung lived a long time - he died in 1961 at the age of 86 - and partly because Jung, unlike Freud, was an extremely active man. It is also an old-fashioned story, as Jung would have liked it to be: a 19th-century tale of the loss of religious belief and the quest for a good life without the traditional sops and guidelines. Not exactly Modern Man's Search of a Soul - one of Jung's chararacteristically high-flying and far-flung titles - but modern man's search for something to believe in to keep himself going.

Jung ended up calling it individuation - the now familiar willingness to become oneself, with the assumption that one has a self to become - but it was called different things throughout his life: his number two personality, his father (never his mother), Nietzsche, the unconscious, Freud, psychoanalysis, analytical psychology, alchemy, the collective unconscious, the soul. Jung's life, which is remarkable if only for the tenacity with which he struggled with himself, captures the imagination of people for whom life is only valuable, or even bearable, if they can find meaning in it.

Unsurprisingly perhaps, Jung's hunger for meaning, which allowed him to take religion rather more sympathetically then Freud did, was not always compatible with his over-stressed wish to be a scientist of the soul. Jung, in other words - and Bair's words are often instructive - is a magnet for many of our contemporary preoccupations; above all, how we have come to believe that we need to believe in something (or someone) in order to have good-enough lives. And why it is that once we want to believe, we are drawn to believe in the supernatural; in something that by definition has to be so much more powerful than we are ourselves. Jung seems to have suffered a life-long, catastrophic disillusionment that he was only a person. His remarkable work was a quest, among other things, to compensate for this.

The only son of two people who were both the 13th child in their respective families, Jung seems to have been born with a sense of ominous uniqueness. His mother, in Bair's vivid account, was an extremely unhappy, lonely and haunted woman. His adored father was a more or less failed Swiss pastor, a melancholic man of esoteric interests. Like everyone else Jung sounds like an uncanny combination of his parents: growing up with so much disappointment and supersitition - two things that often go together - he found at first philosophy (Kant, Schopenhauer and Nietzsche) and then the newish science of psychiatry as at once a refuge from, and a bulwark against, his family. As a man very much of his time, with a fin-de-siècle appetite for the new that was also a cover-up for an obsession with the past, Jung both found and invented the then not so well-known Freud.

Inevitably Bair's biography is, like all the previous biographies of Jung, a before and after life in which he struggles to find himself, thinks he has found himself in Freud, and eventually becomes himself by recovering from his troubled relationship with the man he hoped would be his master. But Bair, rightly, sees that there was far more to Jung than his life-changing (and inevitable) disappointment with Freud. If her clichéd misgivings about Freud implicitly make Jung seem naive for having been impressed by this sex-obsessed authoritarian bigot, her one-sided approach at least has the merit of refusing to make Jung a footnote to psychoanalysis. Just as there was more to Freud than psychoanalysis, there was far more to Jung than his interest in Freud. Jung did the thing that most of Freud's followers were unable to do, and therefore never forgave him for doing: he made use of Freud's work without becoming a Freudian. That the idolator became an idol himself is, as ever, the sadder story. Jung himself ended up in need of more disciples than was good for him.

Throughout his life Jung was fearful about being misunderstood. What Bair refers to as the circularity in his writing - literally the way Jung, by his own admission, kept going round in circles, apparently uninterested in sequential argument - dismayed Jung himself. Each of his writings was, he wrote, "the attempt to bring the unsayable of the background into the objective world of science. All my works are commissions from the inside, so to speak."

Jung was adept at making people feel that there were amazing things inside them, things of cosmic significance. And unlike Freud, Jung knew from his own experience what it was to be really mad. He was never quite sure which of the two versions of himself he was most impressed by: the inspired, tormented eccentric, or the respectable, assured, bourgeois professional. What Bair intimates in her even-handed way is that we should not be quite as fascinated as Jung was by his own depths. That we might, for example, take seriously the fact that he married into one of the richest families in Switzerland; that he was overly impressed by all things English, especially the aristocracy; and that he had a passion for glamorous cars. Jung's lifelong fear of being misunderstood was more of an insistence that he be taken only on his own terms. When Freud described Jung's book Psychological Types as "the work of a snob and a mystic", he may have underestimated just how important snobs and mystics were to Jung. Indeed Jung's work seems to suggest, often unwittingly, that mysticism is itself a form of snobbery, that spirituality might be the new elitism.

What people tend to want to know now about Jung is whether he was a Nazi sympathiser, and whether he was a womaniser. Bair is diligent and temperate in her examination of Jung's putative anti-semitism and implies, without quite saying so, that he was not a Nazi collaborator, and that to raise issues of racial identity, as Jung was more than keen to do, does not, in and of itself, make one a racist. That there are false notes and open questions here she never denies. About Jung's relationship with women she is far more reticent, though it is perhaps worth noting that she often makes Jung's wife, Emma, sound far more interesting than her husband.

If the question we are likely to ask of Freud now is "why was he so interested in sexuality?", the question we are likely to ask of Jung is "why was he so interested in himself?" Bair gives us lots of leads. And, like Jung himself, she has tried to be rather more empirical than speculative in her account. But the more we know about Jung the less real he becomes. About why this should be so, we can only speculate.